In 1904, Ludwig Prandtl derived the exact mathematical conditions for flow separation to occur. But his work had two major restrictions: first, it applied only to steady flows, such as those around a car moving at a constant low speed. Second, it only applied to idealized two-dimensional flows.

"Most engineering systems, however, are unsteady. Conditions are constantly changing," George Haller, a visiting professor in the MIT Department of Mechanical Engineering said. "For example, cars accelerate and decelerate, as do planes during maneuvers, takeoff and landing. Furthermore, fluids of technological interest really flow in our three-dimensional world," he added.

As a result, ever since 1904 there have been intense efforts to extend Prandtl's results to real-life problems, i.e., to unsteady three-dimensional flows.

A century later, Haller led a group that did just that. In 2004 Haller published his first paper in the Journal of Fluid Mechanics explaining the mathematics behind unsteady separation in two dimensions. This month, his team reports completing the theory by extending it to three dimensions. Haller's coauthors are Amit Surana, now at United Technologies; MIT student Oliver Grunberg; and Gustaaf Jacobs, now on the faculty at San Diego State University.